WKB analysis for nonlinear Schrödinger equations with potential

We justify the WKB analysis for the semi-classical nonlinear Schrödinger
equation with a sub-quadratic potential. We present the geometrical and
analytical tools which may be used to study the role of the potential and
the nonlinearity respectively. In the last case we present, we construct
solutions for some compressible Euler equations with unbounded source term
and unbounded initial velocity.